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According to a Pew Research Center, in May 2011, 35% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.

She selects 300 community college students at random and finds that 120 of them have a smart phone. In testing the hypotheses: H0: p = 0.35 versus Ha: p > 0.35, she calculates the test statistic as Z = 1.82.

Use the Normal Table to help answer the p-value part of this question.

Click here to access the normal table.

1. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).

2. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.068).

3. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.966).

4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).

User Arinte
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1 Answer

7 votes

Answer:


p_v =P(z>1.82)=0.034

Assuming a standard significance level of
\alpha=0.05 the best conclusion for this case would be:

4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).

Because
p_v <\alpha

If we select a significance level lower than 0.034 then the conclusion would change.

Explanation:

Data given

n=300 represent the random sample taken

X=120 represent the people who have a smart phone


\hat p=(120)/(300)=0.4 estimated proportion of people who have a smart phone


p_o=0.35 is the value that we want to test

z would represent the statistic (variable of interest)


p_v represent the p value (variable of interest)

System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion of people who have a smart phone is higher than 0.35, the system of hypothesis are.:

Null hypothesis:
p\leq 0.35

Alternative hypothesis:
p > 0.35

The statistic is given by:


z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}} (1)

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:


z=\frac{0.4 -0.35}{\sqrt{(0.35(1-0.35))/(300)}}=1.82

Statistical decision

Since is a right tailed test the p value would be:


p_v =P(z>1.82)=0.034

Assuming a standard significance level of
\alpha=0.05 the best conclusion for this case would be:

4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).

Because
p_v <\alpha

If we select a significance level lower than 0.034 then the conclusion would change.

User Theutz
by
8.1k points
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